itdr-vignette

Overview

itdr is a system for estimating a basis of the central and central mean subspaces in regression by using integral transformation methods. This vignette demonstrate the usage of functions in itdr package over automobile, Recumbent and PDB datasets.

Chapter 1: Installation

1.1: Install itdr package

Installation can be done for itdr R package in three ways.

• From the Comprehensive R Archive Network (CRAN): Use install.packages() function in R. Then, import itdr package into working session using library() function. That is,
install.packages("itdr")
library(itdr)
• From binary source package: Use intall.package() function in R. Then, import itdr package into working session using library() function. That is,
install.packages("~/itdr.zip")
library(itdr)
• From GitHub: Use install_github() function in R devtools package as follows.
library(devtools)
install_github("TharinduPDeAlwis/itdr")
library(itdr)

Acknowledgment

The codes for the Fourier transformation and the convolution transformation methods are adapted from the codes provided by Zhu and Zeng (2006). Moreover, those for the elliptically contoured distributed variables and the kernel density estimation methods are essentially a modification of the program provided by Zeng and Zhu (2010). The code for Fourier transforms approach for the inverse dimension reduction method is adapted from the code provided by Weng and Yin (2018).

References

• Bentler, P.M., and Xie, J. (2000). Corrections to Test Statistics in Principal Hessian Directions. Statistics and Probability Letters. 47, 381-389.

• Cook R. D., and Li, B., (2002). Dimension Reduction for Conditional Mean in Regression. The Annals of Statitics, 30, 455-474.

• Weng J. and Yin X. (2018). Fourier Transform Approach for Inverse Dimension Reduction Method. Journal of Nonparametric Statistics. 30, 4, 1029-0311.

• Zeng P. and Zhu Y. (2010). An Integral Transform Method for Estimating the Central Mean and Central Subspaces. Journal of Multivariate Analysis. 101, 271–290.

• Zhu Y. and Zeng P. (2006). Fourier Methods for Estimating the Central Subspace and Central Mean Subspace in Regression. Journal of the American Statistical Association. 101, 1638–1651.